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Came across this question in a children's recreational mathematics book. Apparently, the cross section of a cube cannot be a regular pentagon. It could be a irregular pentagon though.

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But if we generalize this problem, can the cross section of parallelepiped be a regular pentagon? How do we prove that?

Helen
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1 Answers1

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No, it's impossible. Consider two sides of the pentagon that lie in opposite faces of the parallelepiped. The sides lie in the plane of the pentagon, and they also lie in two parallel planes, so they must themselves be parallel, but a regular pentagon has no parallel sides.

saulspatz
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